Manifolds and heteroclinic connections in the Lorenz system
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Tue, 22/11/2005 16:30 |
Dr Hinke Osinga (University of Bristol) |
Applied Dynamical Systems Seminar  |
Dobson Room, AOPP |
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The Lorenz system still fascinates many people because of the simplicity of the
equations that generate such complicated dynamics on the famous butterfly
attractor. The organisation of the dynamics in the Lorenz system and also how
the dynamics depends on the system parameters has long been an object of study.
This talk addresses the role of the global stable and unstable manifolds in
organising the dynamics. More precisely, for the standard system parameters, the
origin has a two-dimensional stable manifold and the other two equilibria each
have a two-dimensional unstable manifold. The intersections of these two
manifolds in the three-dimensional phase space form heteroclinic connections
from the nontrivial equilibria to the origin. A parameter-dependent study of
these manifolds clarifies not only the creation of these heteroclinic
connections, but also helps to explain the dynamics on the attractor by means of
symbolic coding in a parameter-dependent way. This is joint work with Eusebius Doedel (Concordia University, Montreal) and Bernd Krauskopf (University of Bristol). |
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